Basic Statistics:
 Random numbers. Probability. Moments. Generating function.
 Independence. Law of large numbers (strong and weak versions). Central Limit Theorem. Large Deviation and Cramer function. Sigma algebra operations.
Foundations of information theory:
 Multivariate distributions. Marginalization. Conditional Probabilities. Bayes theorem.
 Entropy, independence, mutual information, comparison of probabilities (KullbackLeibler)
 Probabilistic inequalities for entropy and mutual information
 Information channel. Shannon Theorem.
 Thermodynamic potentials and free energies, thermodynamic formalism in information theory.
Markov Chains [discrete space, discrete time]:
 Transition probabilities. Properties of Markov Chains. Steady State Analysis.
 Spectrum of the Transition Matrix & Speed of convergence (to steady state)
 Reversible and Irreversible Markov Chains. Detailed vs Global Balance.
 Exactness and convergence. PerronFrobenius (connect to linear algebra) and implications for Markov chains.
